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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

Interior angle sum = (n − 2) × 180°. The exterior angles of any convex polygon add to 360°.

1.Find the size of each interior angle of a regular 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
2.Each exterior angle of a regular polygon is 72°. How many sides does it have?

Answer: 5

  1. Exterior angles add to 360°
  2. 360 ÷ 72 = 5 sides
3.The interior angles of a quadrilateral are 108°, 73°, 108° and x°. Find x.

Answer: 71°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 108 − 73 − 108 = 71
4.Each interior angle of a regular polygon is 160°. How many sides does it have?

Answer: 18

  1. Each exterior angle = 180° − 160° = 20°
  2. 360 ÷ 20 = 18 sides
5.The interior angles of a polygon add up to 1,260°. How many sides does it have?

Answer: 9

  1. (n − 2) × 180 = 1,260
  2. n − 2 = 1,260 ÷ 180 = 7, so n = 9
6.Find the size of each interior angle of a regular dodecagon.

Answer: 150°

  1. Angle sum = (12 − 2) × 180° = 1,800°
  2. 1,800° ÷ 12 = 150°
7.Each exterior angle of a regular polygon is 30°. How many sides does it have?

Answer: 12

  1. Exterior angles add to 360°
  2. 360 ÷ 30 = 12 sides
8.The interior angles of a pentagon are 156°, 74°, 87°, 76° and x°. Find x.

Answer: 147°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 156 − 74 − 87 − 76 = 147
9.Each interior angle of a regular polygon is 108°. How many sides does it have?

Answer: 5

  1. Each exterior angle = 180° − 108° = 72°
  2. 360 ÷ 72 = 5 sides
10.The interior angles of a polygon add up to 2,520°. How many sides does it have?

Answer: 16

  1. (n − 2) × 180 = 2,520
  2. n − 2 = 2,520 ÷ 180 = 14, so n = 16
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